Finite Group Databasebeta

← #32985128

Subgroups — #32985128

Order 18688.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618232C211yesmaximal, characteristic
2#22609911C211yesmaximal, characteristic, complemented
3C2×#17988323C212yesmaximal, complemented
4C2×#17988320C212yesmaximal
5C73×#1434C211yesmaximal, characteristic, complemented
6C2×#14556579C411yescharacteristic, complemented
7C2×#14556570C2211yescharacteristic
8C2×#14556565C2211yescharacteristic
9C2×C4⋊#10596831—21no—
10C2×C22⋊#10596831C2212yes—
11#17988493C411yescharacteristic, complemented
12#17988489C411yescharacteristic, complemented
13#17988478—21no—
14#17988478—21no—
15#17988466—21no—
16#17988466—21no—
17#17988453C411yescharacteristic, complemented
18#17988342—21no—
19#17988323—24no—
20#17988320—24no—
21C22×C42×C73C2211yescharacteristic
22C2×#95×C73—21no—
23C2×#95×C73—21no—
24C2×#95×C73C2212yes—
25C22×Dic146C2×C411yescharacteristic
26C22×D292C2×C411yescharacteristic
27C22×C22⋊D73—21no—
28C22×#10596831—22no—
29#14556579—42no—
30#14556570—22no—
31#14556570—22no—
32#14556565—22no—
33#14556565—22no—
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924007—21no—
37C2×C22⋊Dic73—21no—
38C2×#11924005—21no—
39C2×#11924005—21no—
40C2×#11924005—21no—
41C2×#11924005—21no—
42C2×#11924005—21no—
43C4⋊#10596831—42no—
44C22⋊#10596831—22no—
45C22⋊#10596831—22no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50C23×C4×C73—22no—
51C23×C4×C73D411yescharacteristic
52C23×C4×C73D411yescharacteristic
53C23×C4×C73C2311yescharacteristic
54C2×C42×C73—42no—
55C2×C42×C73C2×C411yescharacteristic
56C2×C42×C73C2×C411yescharacteristic
57C2×C42×C73D411yescharacteristic
58C2×C42×C73D411yescharacteristic
59#95×C73—22no—
60#95×C73—42no—
61#95×C73—42no—
62#95×C73D414yes—
63C23×D73—21no—
64C2×Dic146—22no—
65C2×Dic146—41no—
66C2×Dic146—41no—
67C2×D292—22no—
68C2×D292—41no—
69C2×D292—41no—
70C2×C22⋊D73—42no—
71C2×C22⋊D73—42no—
72C2×C22⋊D73—41no—
73C2×C22⋊D73—41no—
74C22×Dic73—21no—
75C22×Dic73—21no—
76C22×Dic73—21no—
77C2×#10596831—42no—
78C2×#10596831—42no—
79C2×#10596831—42no—
80C4⋊Dic73—22no—
81C4⋊Dic73—22no—
82#11924007—41no—
83#11924007—41no—
84C22⋊Dic73—42no—
85#11924005—42no—
86#11924005—42no—
87#11924005—42no—
88#11924005—42no—
89#11924005—41no—
90#11924005—41no—
91C24×C73C2×D411yescharacteristic
92C22×C4×C73—22no—
93C22×C4×C73—21no—
94C22×C4×C73—21no—
95C22×C4×C73—22no—
96C22×C4×C73—24no—
97C22×C4×C73—41no—
98C22×C4×C73—41no—
99C22×C4×C73—41no—
100C22×C4×C73—41no—
101C22×C4×C73—41no—
102C22×C4×C73—42no—
103C22×C4×C73—42no—
104C22×C4×C73—42no—
105C22×C4×C73—42no—
106C22×C4×C73—42no—
107C22×C4×C73—42no—
108C22×C4×C73C22⋊C411yescharacteristic
109C22×C4×C73C22⋊C411yescharacteristic
110C22×C4×C73C22⋊C411yescharacteristic
111C22×C4×C73C22⋊C411yescharacteristic
112C22×C4×C73C22×C411yescharacteristic
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73C2×D412yes—
115C22×C4×C73#4112yes—
116C42×C73—22no—
117C42×C73—22no—
118C42×C73—41no—
119C42×C73—41no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73C2×C22⋊C411yescharacteristic
125C23×C73#12112yes—
126C23×C73#13512yes—
127C23×C73AGL(1,ℤ/8)11yescharacteristic
128C23×C73#13711yescharacteristic
129C22×D73—41no—
130C22×D73—41no—
131C22×D73—41no—
132C22×D73—41no—
133C22×D73—41no—
134C22×D73—41no—
135C22×D73—41no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—42no—
152C2×C4×C73—42no—
153C2×C4×C73—44no—
154C2×C4×C73—42no—
155C2×C4×C73—42no—
156C2×C4×C73—44no—
157C2×C4×C73—44no—
158C2×C4×C73—44no—
159C2×C4×C73—82no—
160C2×C4×C73—82no—
161C2×C4×C73—82no—
162C2×C4×C73—82no—
163C2×C4×C73#9912yes—
164C2×C4×C73C4×D412yes—
165C2×C4×C73#12411yescharacteristic
166C2×C4×C73#12711yescharacteristic
167C22⋊D73—82no—
168C22⋊D73—82no—
169C2×Dic73—41no—
170C2×Dic73—41no—
171C2×Dic73—41no—
172C2×Dic73—41no—
173C2×Dic73—41no—
174C2×Dic73—41no—
175C2×Dic73—41no—
176C2×Dic73—41no—
177C2×Dic73—41no—
178D292—82no—
179Dic146—82no—
180#10596831—82no—
181C22×C73—22no—
182C22×C73—22no—
183C22×C73—21no—
184C22×C73—21no—
185C22×C73—21no—
186C22×C73—21no—
187C22×C73—22no—
188C22×C73—22no—
189C22×C73#39011yescharacteristic
190C22×C73C2×#9911yescharacteristic
191C22×C73#41011yescharacteristic
192C22×C73#41611yescharacteristic
193C22×C73#41711yescharacteristic
194C22×C73#42111yescharacteristic
195C22×C73#42111yescharacteristic
196C22×C73#46312yes—
197C22×C73#46412yes—
198C2×D73—81no—
199C2×D73—81no—
200C2×D73—81no—
201C2×D73—81no—
202C2×D73—81no—
203C2×D73—81no—
204C2×D73—81no—
205C4×C73—21no—
206C4×C73—22no—
207C4×C73—21no—
208C4×C73—22no—
209C4×C73—41no—
210C4×C73—41no—
211C4×C73—41no—
212C4×C73—84no—
213Dic73—81no—
214Dic73—81no—
215Dic73—81no—
216#9716—731nomaximal, Sylow
217C2×C73—22no—
218C2×C73—22no—
219C2×C73#151211yescharacteristic
220C2×C73#151311yescharacteristic
221C2×C73#151611yescharacteristic
222C2×C73#152111yescharacteristic
223C2×C73#196311yescharacteristic
224C2×C73#196411yescharacteristic
225C2×C73#198311yescharacteristic
226D73—161no—
227#2850—731no—
228#1797—731no—
229C2×#328—732no—
230C2×#327—732no—
231#1434D7311yescharacteristic, complemented
232C73#971611yescharacteristic, complemented, Sylow
233C2×#124—731no—
234C2×C22⋊Q8—731no—
235C2×#121—731no—
236C22×C42C2×D7311yescharacteristic
237C2×C4⋊C8—1461no—
238C2×C22⋊C8—732no—
239#391—731no—
240#390—731no—
241#388—1461no—
242#388—1461no—
243#386—1461no—
244#386—1461no—
245#382—731no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95C2×D7312yes—
249#336—1461no—
250#328—1464no—
251#327—1464no—
252C22×Q8—731no—
253C22×D4—731no—
254C22×D4—1461no—
255C23×C4—22no—
256C23×C4C22⋊D7311yescharacteristic
257C23×C4C22⋊D7311yescharacteristic
258C23×C4C22×D7311yescharacteristic
259C22×C8—1462no—
260#124—2922no—
261C22⋊Q8—1462no—
262C22⋊Q8—1462no—
263#121—1462no—
264#121—1462no—
265C2×C4⋊C4—731no—
266C2×C4⋊C4—731no—
267C2×C4⋊C4—1461no—
268C2×C22⋊C4—1461no—
269C2×C22⋊C4—1461no—
270C2×C22⋊C4—1461no—
271C2×C22⋊C4—1461no—
272C2×C22⋊C4—1461no—
273C2×C22⋊C4—1461no—
274C2×C42—42no—
275C2×C42C4×D7311yescharacteristic
276C2×C42C4×D7311yescharacteristic
277C2×C42D29211yescharacteristic
278C2×C42D29211yescharacteristic
279C4⋊C8—2922no—
280C22⋊C8—1462no—
281C22⋊C8—1462no—
282#95—22no—
283#95—42no—
284#95—42no—
285#95—1461no—
286#95—1461no—
287#95—1461no—
288#95—1461no—
289#95D29214yes—
290C24—1461no—
291C24C2×C22⋊D7311yescharacteristic
292C2×Q8—2921no—
293C2×Q8—2921no—
294C2×Q8—1462no—
295C2×D4—2921no—
296C2×D4—2921no—
297C2×D4—2922no—
298C2×D4—2922no—
299C2×D4—2921no—
300C2×D4—2921no—
301C2×D4—1462no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—1461no—
319C22×C4—1461no—
320C22×C4—1461no—
321C22×C4#1192400511yescharacteristic
322C22×C4#1192400511yescharacteristic
323C22×C4#1192400511yescharacteristic
324C22×C4#1192400511yescharacteristic
325C22×C4C2×C4×D7311yescharacteristic
326C22×C4C2×D29211yescharacteristic
327C22×C4C2×D29212yes—
328C22×C4#1192402812yes—
329C2×C8—2922no—
330C2×C8—2922no—
331C2×C8—2922no—
332C4⋊C4—2921no—
333C4⋊C4—2921no—
334C4⋊C4—1462no—
335C4⋊C4—1462no—
336C22⋊C4—2922no—
337C22⋊C4—2922no—
338C22⋊C4—2922no—
339C22⋊C4—2922no—
340C22⋊C4—2922no—
341C22⋊C4—2921no—
342C22⋊C4—2921no—
343C42—22no—
344C42—22no—
345C42—41no—
346C42—41no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—2921no—
352C23—2921no—
353C23—2921no—
354C23—2921no—
355C23—2921no—
356C23—2921no—
357C23—2921no—
358C23C2×#1192400511yescharacteristic
359C23#1455656512yes—
360C23#1455661112yes—
361C23#1455661711yescharacteristic
362C23#1455662211yescharacteristic
363Q8—5842no—
364D4—5842no—
365D4—5842no—
366D4—5842no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—2921no—
395C2×C4—2921no—
396C2×C4—2921no—
397C2×C4—2921no—
398C2×C4—2921no—
399C2×C4—2921no—
400C2×C4—2921no—
401C2×C4—2921no—
402C2×C4—2921no—
403C2×C4#1455650512yes—
404C2×C4C4×D29212yes—
405C2×C4#1455657911yescharacteristic
406C2×C4#1455658811yescharacteristic
407C8—5842no—
408C22—22no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—22no—
416C22—5841no—
417C22—5841no—
418C22—5841no—
419C22—5841no—
420C22—5841no—
421C22—5841no—
422C22—5841no—
423C22#1798848911yescharacteristic
424C22C2×#1455650511yescharacteristic
425C22#1798856011yescharacteristic
426C22#1798858111yescharacteristic
427C22#1798858611yescharacteristic
428C22#1798860511yescharacteristic
429C22#1798860511yescharacteristic
430C22#1798880212yes—
431C22#1798880912yes—
432C4—21no—
433C4—22no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—5841no—
441C4—5841no—
442C4—5841no—
443C2—22no—
444C2—22no—
445C2—11681no—
446C2#2260846711yescharacteristic
447C2#2260847211yescharacteristic
448C2#2260848511yescharacteristic
449C2#2260850611yescharacteristic
450C2#2261076311yescharacteristic
451C2#2261076711yescharacteristic
452C2#2261086311yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1434C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556565C22
cosocleC23×C4×C73C23
hypercenter#1434D73
hypocenterC73#9716
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22609911C2semidirect
3. C2×#17988323C2semidirect
5. C73×#1434C2semidirect
6. C2×#14556579C4semidirect
11. #17988493C4semidirect
12. #17988489C4semidirect
17. #17988453C4semidirect
231. #1434D73semidirect
232. C73#9716semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226182322
#226099112
C2×#179883232
C2×#179883202
C73×#14342
#971673